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Friday, July 31, 2009

On page 132 of his 2000 paper with Worley and Bernstein (really page 16 of the article), they note:

"But in cognition, the problem itself sometimes is to entertain a representationalstate with appropriate content. Representing the appropriate ‘‘target state’’ isthe whole point of the process. Vector subtraction is inappropriate for these processesbecause it requires that the goal (future ‘‘targets’’) already be represented. (In ourneurocomputational model, this representation is the set of values in the Next TargetNodes.) Hence vector subtraction is unnecessary for this type of cognitive problem.Whatever computation is supplying the values to the Next Target Nodes is doing thework." (my emphasis)

I think that vector subtraction may still play a role in "entertain[ing] a representational state with appropriate content," via the process I suggested in the my last post on Bickle. That is: if the vector for moving from point A to B is stored in memory, it can be used as directions from any other known point C to an unknown point or "sub-volume" D. By using the stored instruction A->B from point C, point (or volume) D is discovered or created.

I think this helps answer the implied question in "Whatever computation is supplying the values to the Next Target Nodes is doing the work." Point D can be discovered via the process in the paragraph above, then the vector B->D can be discovered by ordinary vector subtraction.

... I'm on page 16 of the paper, so maybe that idea will be addressed later on.

Their two rationales were to 1) stimulate new auto sales and 2) get old, inefficient cars off the road and replaced with newer more efficient ones.

The first rationale is an interesting answer to public backlash over bailouts. It makes it look like the government is handing out money to the people, rather than straight to the car companies. Never mind that once you've got your $4.5K from the government, you're on the hook to pay for the rest of the car. So really, you've just been encouraged to subsidize car companies from your wallet, rather than your income tax. And please ignore the fact that the government'll be needing that $4.5k back at some point, since they had to borrow it from the ever-generous developing world and eventually the loans will come due. There's a reason Bernie Madoff is in prison; we should hold our politicians to the same standard of accountability.

The second rationale looks pretty sound on the surface, but remember that it takes energy and resources to build a new car, and any remaining use you could have extracted from the clunker (maybe by doing regular maintenance on it) is wasted. In other words: when you consider the whole life cycle of a vehicle, it's less efficient to buy a new one with good gas mileage than an old one with poor mileage. One might object that they could save more money on gas than the price difference between the new and the old car... but the math doesn't tend to work out in that person's favor, given the outstanding rate of depreciation on new cars. I imagine that the existing capital stock of vehicles could be maintained indefinitely, adding new ones only to satisfy growing numbers of drivers in the market (like we do with airplanes), but at some point we as a society decided that we'd rather throw our great masses of steel, glass, and rubber away every five years and have new ones made for ourselves. And the auto companies happily complied, producing vehicles that matched our expectancies in terms of lifespan.

It didn't have to be that way. Again, look at the aviation market. Planes are much more complex machines, and they stay in service for much much longer. I imagine that has a lot to do with lawfully required maintenance programs. What if it regular preventative maintenance on parts that are known to wear out after so many uses was required for cars, just like it is for airplanes? Oh, and what if instead of letting the government do that, we privatized all the roads, and let the owners decide what standards they want to require from their clients? Set up software that schedules and tracks the maintenance of each vehicle and a system of trust certificates that can be used for verification. You're maintenance bill would be higher, but your new-car-every-five-years bill would be zero. Plus the roads would be safer.

Not likely to get implemented any time soon.

That the program is being axed because it spent its entire budget in one week is ironic icing on the cake of centrally-planed ineptitude.

Update: well, I guess congress extended its funding by another $2,000,000,000 ($2B). True; that's a drop in the bucket next to the $1,000,000,000,000 ($1,000B+) we've spent in other bailouts, but if the program maintains its popularity, they'll have to keep re-authorizing that amount every two weeks. Fifty Two Billion is bigger than the bailout we gave to GM.

Before I read it, I want to record what I think is a novel and useful idea, so that if it comes up in the paper I can pat myself on the back (publicly) for having thought of it independently.

Regarding the neural basis of analogy-making, which was the topic of my final paper for Bickle, I have an idea how analogies might be formed using the vector subtraction paradigm. Reference my previous post to get a feel for what I'm talking about.

If you are given two initial points, you can calculate the vector that directly connects them. The connecting vector is the instruction for getting from point A to point B. If you are given a third point C, and asked to "do the same thing," you can move use the instruction from the first set of points to move from point C to an unknown point D. Thus, you've made a simple visual analogy.

If the dimensions involved are properties of things (eg tallness, heavyness, hotness...) the same calculations could be used to make a physical/verbal analogy. Omitting some dimension (or leaving it variable) would be the equivalent of "slipping" in Hofstadter's sense, and would allow the destination point D to fall across a range of values. If one of those values falls within the "conceptual halo" of an existing concept, then that concept can be used to complete the analogy. Otherwise a new concept can be created at the destination point, with a "halo" that's defined by the range of values that were suggested by allowing dimensions in the directional vector to remain variable.

Why is this important? If you give credence to the notion that analogy-is-creativity-is-intelligence, then this account goes a very long way in explaining the neural basis for human intelligence. I note that Jeff Hawkins makes this claim also (on pg 183 of On Intelligence). It could also be used as a a guide to identifying cognition in other systems, and in designing it.

Its such a simple elegant explanation!

Its very deeply rewarding to be able to draw connections between disparate authors (in this case Hofstadter, Baum, Hawkins, and Bickle), especially because I don't see any references to each other in their work. It seems implausible that they'd all be unaware of each other... I wonder if the non-citation is a result of dislike or disagreement?

Monday, July 27, 2009

I've been reading Bickel's Philosophy and Neuroscience, A Ruthelessly Reductive Account, and today I've come across a holy grail.

Individually, neurons are performing thresholded temporal summation. This I've known for a while (and I learned the explicit mechanisms for it in Bickel's class last quarter). As compelling as the evidence for these mechanisms is, I hadn't yet heard any good explanation of how this temporal thresholded summation acts in concert with other cells doing the same thing to result in complex memories and actions (though Jeff Hawkins has some insight, from a different approach).

What I learned from Bickel's book today is this: in groups, neurons are performing vector subtraction.

Pretty neat theory, but what's amazing is that Bickel demonstrates this empirically with saccade-sequencing (in two dimensions). That is to say: the instructions for moving the eyes from one point in two dimensional space (say <3,10>) to another point (say <12,8>) are found by summing the negative of the first point and the second point (thus, the vector <9,-2> is found, which are the instructions for moving from the first point to the second point in a straight line). Where does the negative portion come in? Separate sets of neurons fire before and after a saccade, their outputs are always opposed. Thus, after the first the move to <3,10> is executed, a representation of its opposite fires: . By summing this opposite coordinate with the next coordinate <12,8>, the needed path is obtained (again, <9,-2>).

Bickel posits that this may be a general model for all neural processes involving sequencing. This would include body movement (in three dimensions) and speach (in how many dimensions?).

My question: how are things (like speech) that don't have obvious dimensional properties dimensionalized? What is the dimensionality of verbal space? (I think that can be re-phrased as "how many variables does speach involve?" ) Is it consistent across human individuals? Is it something fixed and absolute (like three dimensional space) that humans have to discover through experience and experimentation? Has the experimentation been done over evolutionary time, so that the structure of language-space is encoded in our DNA? Or is it non-absolute and variable between people with different levels of education and methods of thought?

I think the former is Chompsky's position (as well as Baum's), whereas the latter seems to be more intuitively plausible given the understanding that cortical material is uniform (ala Hawkins). Godel's essential incompleteness also seems to suggest that there is no ultimate, perfect space of language, since reflecting on the existing space creates a new dimension as many times as one cares to do the reflection, infinitely.

Maybe a simpler question: how many dimensions are neural systems capable of representing? Do three-dimensional movements get collapsed into two? Or are there arbitrarily many superflous, greater dimensions involved?

[Update: Churchland speculates that one dimension per neuron can be represented, plus gradients for synaptic weights and firing rates. So the representative capacity is somewhere above 10^100 (a googol) distinct concepts... greater than the number of elementary particles in the universe. Mind-bender, eh? That's not to say that we actually have that many distinctly stored concepts, just that that's the theoretical capacity. The truth is that the fine-grained differences are probably not important]

Saturday, July 25, 2009

Rachael and I saw the opera Carmen for the second time last night, and it was excellent.

Most opera I've been to, including Carmen the first time, has been more occasion to exercise endurance than to experience pleasure. I've figured that I should make an attempt to appreciate this lasting artform that so much effort goes into, and which seems to be widely enjoyed by cultured, intelligent folk. It may be that I'm a bit lacking in those qualities, but I've been nonplussed by the cliched love stories and ornamented performance that has seems endemic to the medium.

Ah, but this Carmen was different. I felt the danger on the stage, the jealous insanity, the exasperation, the integrity of character. I'm not sure what was different; it may truly be just that we sat on the balcony near the stage (rather than on the orchestra level), and I could actually appreciate the performance. I may have missed the emotional significance of previous operas just by being in a poor position to receive the signals. Or, this one might have just been that much better in it's directing and performance. I would say that the story was much more compelling, but again, I saw it a few years ago and was much less moved.

Either way it's re-invigorated my interest in a medium that I was ready to write off and give up on.

Come to think of it, there are a fair number of opera performances that I've enjoyed. I think this would be the list:

La Finta GiardinieraTurn of the Screw[the opera in english that Danielle performed in... I forget the name]FaustPoe [to some extent, retrospectively]La Boheme

I suppose that's about a quarter of all I've seen, so maybe opera's track record with me isn't so bad.

Skateboards were invented to simulate the feeling of surfing when the surf wasn't up. As an object, it's an expression of hedonic values; it exists to provide a sensation that's valuable in and of itself as perceived by (certain) humans. Its counter cultural connotations probably arise from the fact that skating (and surfing) benefit no one but the person doing it; especially since it's a solo sport and can't be said to facilitate social bonding like team sports do.

Whereas surfing is all about water, skateboarding has come to be associated with air as a result of the types of tricks that lend themselves to skating. This is despite the fact that it's an earthbound vehicle, and limited, impractical one at that. Those who make skating into an art form seem to be elegantly turning the constraining force of gravity into a tool to escape from it, transiently.

I think this desire for transcendence is neatly expressed by painting wings on a wheeled plank. It reflects an awareness of the limitations, and a childish flouting of them. Naive and innocent; just daring enough to challenge what's accepted as truth.

Skaters often keep their broken boards, perhaps as evidence of their daring. They can also be seen as symbols of consequence: experimenters put themselves at risk of unknown dangers. Brave experimenters are aware of the risk of the unknown, and seek to discover and overcome it.

So what does this broken, winged skateboard say? I say it's an expression of an attempt to transcend the bonds of fear and turn the forces of nature into tools of one's will. That it's broken says that experimenters will fail; that it's put together again says they will be undaunted and try again.

In the face of the counter cultural symbolism of the skateboard itself, it speaks of experimenting with lifestyles, modes of expression, and core values. But in the end, it's just a broken wooden toy. We must be brave and experiment with new mediums of self-expression as well.

Tuesday, July 21, 2009

I recently discovered that eating raw eggs is healthy, more nutritious, and not likely to give you salmonella poisoning. Its also one of the few foods that seem to digest effortlessly and give you quick energy. I figured out how to flick the top of with my fingernail and eat it straight from the shell. Flavorless, and oddly satisfying.

I also tested the hypothesis that eating a kiwi with the peel still on is a reasonable thing to do. Turns out: true. I always thought the idea was really weird, but I find that its much more convenient than peeling it, and neither the flavor of the peel nor the texture are detrimental.

Oh, what significant blogging material.

Perhaps more striking: I biked from Clifton to West Chester a couple days ago. Its really only fifteen miles, but they're hilly, bastardly miles. It gave me the confidence that I can do such things with only an acceptable level of discomfort. I'm currently enjoying the benefits of having a testosterone-producing body; the lifting I've done over the last two weeks has produced immediate, noticeable results. I had gotten so out of shape that you could feel my ribs through my pectoral muscles without pressing very hard; now they've got a little more of an appropriate thickness and heft. Protine shakes and creatine pry don't hurt either.

Rick and Matt and I had another good jam session on Sunday, we got some good recordings out of it and created a few new grooves. Its interesting how people seem to be attracted to the music coming out of the gallery, a few people have walked right in and started talking with us (or giving us advice). Its a little annoying to be interrupted, but its neat to be engaging people on the street. I think we need to find a way to bring the people in the neighborhood in to make music; that could be really cool.

I've been deep in relaxation mode the last couple weeks, lots of sleep and not enough work. Need to get re-motivated and disciplined into furthering my learning. I've been thinking more and more about taking the bio and chem courses. Looking back at my all the classes I've taken, Bickel's neuroscience class was by far the one that captured my imagination the most. I should really be in that field, I think... the only question is whether its advisable to go back and take the undergraduate courses or if I should study the subjects at the graduate level while working towards another degree.

Meh. Degrees may not be the best way to judge progress, but I'm not sure what other good metrics there are.

Wednesday, July 15, 2009

-Got the CS13 website online: cs13gallery.com-Got CS13 registered on google maps.-Put all the postcards from the opening show online. Oddly, they seem more interesting when you view them online, one by one. I think having 250 of them on the wall was overwhelming; you ended up not focusing on any of them.-Went to the CS13 reading group, discussed Invisible Cities with Issac and Bill.-Got my TimothyJosephMurphy.com domain registered, started work on the site.-Figured out how to use my sweet (and unnamed) new audio recording to export MP3's, posted the good recordings online (see two posts ago).-Read a bunch of Time Series Forecasting class chapters.-Discovered the Dead Weather; I dig em.-Helped Matt and Jude eat all some of their leftover camping breakfast food.-Went on on a 20 mile bike ride last friday with Issac; I ate too soon before hand and felt like I had a rock in my stomach and no energy. My muscles didn't end up getting sore, I was just exhausted.-I've been working out with Rick; my upper body is super sore.

Tuesday, July 14, 2009

Last month, at the opening, the owner of Iris and Urban Eden commented on one of my t-shirts. She asked if I made them, and I explained my method and what they're supposed to be about. She enthusiastically suggested that I should bring some to her shop, and that she would sell them. I went into Iris on sunday, and Lo! she was wearing one! She bought one and sold two to customers. She said that there were requests for larger and femenine cut shirts, so I'll have to make some of those.

Sunday, July 5, 2009

Markets are information processing mechanisms. Humans ("agents") gather information about the environment and bring it into a forum where their information can be expressed. The form of expression is simple: supply and demand. Agents from some areas will demand certain things, and this is a reflection of the state of the environment in that area. The same goes for supply. Thus, information about the environment is filtered through the needs of the agents and transmitted to other agents, many of whom will never interact directly.

The compression of all possible information into two attributes is interesting by itself. It like a double-binary (quaternary?) code: the existence or absence of two things. I suppose it could be compressed to binary, since an agent can't have both a supply and a demand (of the same object) at the same time. Or perhaps a special case of ternary (base three) with the values -1, 0, and 1 ? Or is that still binary with "two's compliment"?

Memories as Stable Patterns

In neurons, memories are stored by establishing a network of cells that are sensitive to each other's firing, such that when a certain stimulus occurs they will fire in the same pattern. Memories are maintained by keeping the firing pattern active until the connections are strong enough that they will not fade. In other words, the stimulus is re-experienced internally -the memory is replayed after the event- until long-term potentiation establishes the heightened sensitivity.

Can I connect this with the market framework? When a demand is present in enough strength, supply agents will find and satisfy it. When it is persistent, supply agents will build infrastructure that allows them to satisfy the demand at a lower cost. Once the infrastructure is in place, the same patterns of supply and demand will persist until the agents get old and die or the system is shocked. Thus, we have stable patterns of activation in the economic network that reflect the perceived state of the external world. In other words: intentionality.

Can inhibitory neurons be compared to selling agents, and excititory neurons compared to demand agents?

Wednesday, July 1, 2009

Read first 2 sections of The Black Swan. Ironically, it's main point is that both of the classes I'm taking this quarter are at best misleading, and at worst deceptive.

Read Little Brother, by Corey Doctrow. Its awesome.

Almost bought another motorcycle; cb750 for $800. Would have been a good deal, but I decided I should be able to get along with the bicycle, Ricks bike and car, and the motorcylce I have (if I can get it fixed).

Got health insurance. It was much easier than I expected; just walked into the office and signed a form. Not terribly expensive either.